Solve the simultaneous linear inequalities below *
2x - 5 > 11 and x over 3 - 2 is less than or equal to 3
A. 8 ≤ x < 18
B. 8 < x ≤ 18
C. 8 < x ≤ 15
D. 8 ≤ x < 15
Answers
Solution
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Correct option is
C
Quadrant IV
given, y≥2x+1 and
y>
2
1
x−1
first, draw the graph for equations y=2x+1 and y=
2
1
x−1
for y=2x+1
substitute y=0 we get, 2x+1=0⟹x=−0.5
substitute x=0 we get, y=1
therefore, y=2x+1 line passes through (0.5,0) and (0,1) as shown in fig.
Hence, y≥2x+1 includes the region above the line.
for y=
2
1
x−1
substitute y=0 we get,
2
1
x−1=0⟹x=2
substitute x=0 we get, y=−1
therefore, y=2x+1 line passes through (2,0) and (0,-1) as shown in fig.
Hence, y>
2
1
x−1 includes the region above the line.
the intersection region is the shaded region as shown in above figure which includes I, II and III quadrants.
Therefore, quadrant IV has no solution
solution
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SIMILAR QUESTIONS
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Solve the following system of inequalities graphically.
x≥3,y≥2
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>
Graph the solution sets of the following inequations :
x+2y>1.
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